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Evidence For A Shell Origin In Galaxy Formation 9 0 0 2 David E. Rosenberg NJIT Physics Newark NJ n John Rollino Rutgers Physics Newark NJ a J E-mail: [email protected]; c 2009 6 (cid:13) 2 January 26, 2009 3 v 6 6 Abstract 1 8 The galactic correlations of dynamic mass and luminosity, luminosity 0 and color, R50 and R90, MHI and R50, and now surface brightness 0 0 and R50, means that galactic structure must be controlled by a single / parameter. A shell at origin can supply the supermassive black holes h p to form galaxies in a concerted pattern, updated. - o r t 1 Introduction s a : v Although the ΛCDM model is quite successful on supragalactic scales[1], its i X predictions of galactic properties differ markedly with observation. There r has been an excellent fit to observations over 1 Mpc by flat cosmological a models with a mixture of baryons, dark matter and the cosmological con- stant. However, on smaller scales on the order of galaxy and subgalactic, simulations have failed with the assumption that cold dark matter has weak self-interactions and weak baryonic interactions. Cold dark matter should form triaxial halos with dense cores and other dense halo substructures. Yet it has been found that central regions on galactic scales have nearly spherical low density cores. Also dwarf irregular galaxies have low density cores with shallower profiles than predicted. High surface brightness galaxies have per- sistence ofbarsthat implythat galaxiessuch asourownMilky Wayalsohave low density cores. Our Local Group has less than one hundred galaxies while 1 theory and simulations predict about one thousand discrete dark matter halos. These and other problems led Spergel and Steinhardt to propose that there was a ’feedback’ relation so that dark matter could see itself[9]. They proposedcolddarkmatterthatisself-interacting withalargescattering cross section and negligible annihilation or dissipation. Their key proposal was a mean free path in the range of 1 kpc to 1 Mpc at the solar radius, where 3 the dark matter density is 0.4GeV/cm . They estimated dark matter in ≈ the range 1 10000 MeV. After further analysis they came up with a dark − matter particle very much like an ordinary hadron. Although this may solve problems with rotation curves and too numerous sub-clumps in large dark matter halo simulations [7], most of the other difficulties remain. Simulations of galaxy formationusually start with a set of hot gravitating point particles with given initial conditions which are then stepped forward in time using huge computer resources. The Jeans mass is thought to be the point at which gravity overcomes pressure and expansion to form galactic structure. Collapse dynamics produces different post collapse densities, circular speeds and disk asymmetries. The finding that one parameter can describe complex galaxies [6], means that hierarchal galaxy formation is un- tenable. Since this approach has resulted in many virtually insurmountable problems which have been compiled by Sellwood and Kosowsky [7], another approach is necessary for galaxy formation. 2 Model of galaxy formation 2.1 The formation of supermassive galactic black holes In this paper there is an explanation of how a shell of cold matter could became galactic black holes and how the hot expanding core was captured by these newly formed black holes. The deeper the gravitational wells, the higher the velocity and mass of hot hydrogen-helium that could be captured. The finding by Chris Cirilli of large black holes with a much smaller quantity of orbiting hot matter only eight hundred thousand years after the big bang lends additional weight to this concept. One of the earliest spiral galaxy correlations involved the Tully-Fisher relation which originated in 1977. V = 220(L/L ).22 (1) c ⋆ 2 where L is the characteristic spiral galaxy luminosity and V is the circular ⋆ c velocity km/sec. This equation is most accurate in the infra-red range and 4 thus L V . Mass is proportional to luminosity (from captured hydrogen ⋆ ∝ c and helium).The corresponding relation for elliptical galaxies is the Faber- Jackson relation. V = 220(L/L ).25 (2) c ⋆ The Fundamental Plane relations using D σγ has increased the accuracy n ∝ e of Faber-Jackson. The luminous diameter D is defined as the diameter n within the galaxy with mean surface brightness and σ the internal velocity e dispersion. Subsequently, Ferrarese and Meritt found a very tight correlation in both elliptical and spiral galaxies between the galactic supermassive black hole masses M and the velocity dispersions of an elliptical galaxy or the spiral BH bulge velocities σα[3]. M = 1.3 108M (σ /200kmsec−1)4.72±0.36 (3) BH ⊙ c × Ferrarese and Merritt have found that this correlation is so precise that only measurement errors are contained. This then is the fundamental relation for galaxy formation and further work in this paper will be based on it. There are too many close correlations [6], between the dynamical mass and luminosity M L , luminosity and color, radii at 50 percent and radii d g ∝ at 90 percent of emitted light R50 and R90 and the HI mass MHI to R50. The latest relation is the surface brightness is proportional to R50. A more logical starting place is their supermassive galactic black holes. Hot big bang models, with the history of a scale factor close to a singularity, could not produce such galaxies all with such exact correlations. 3 Orbital Dynamics Outside Ten Schwarzschild Radii Outside the immediate area of black hole influence, capturing of matter streaming to the area of influence of each black hole is due to the amount of energy each particle possesses. Large kinetic energies result in hyperbolic or parabolic type orbits with the ability to escape the gravitational well. Lower energies result in stable elliptical or circular orbits. 2 l 1 GmM 2 E = + mr˙ (4) 2mr2 2 − r 3 where E is the total energy, both kinetic and potential. l is the angular momentum, M is the central nuclear mass and and m is the rotational mass. The matter that can be captured will have a total kinetic energy less than the potential energy. Matter with more energy than this, such as hyperbolic or parabolic orbits will be considered as having too much energy for capture in a galactic well of this size. The orbits are differentiated by the following equation from classical mechanics[2] based on the energy and angular momentum. 2El2 e = 1+ (5) s mk2 If e > 1 and E > 0, the orbit is a hyperbola and the matter contains enough energy to escape the galactic well. If e = 1 and E = 0, the orbit is a parabola and the matter may escape. If e < 1 and E < 0, the orbit is an ellipse and the matter has not the energy to escape the galactic gravity. Circular orbits where e = 0 and E = mk2 have even less energy. Since matter that is surely − 2l2 captured has the potential energy greater than the kinetic, 2 GmM l 1 2 > + mr˙ (6) r mr2 2 and e < 1. Expanding the total kinetic energy E in the equation for e, 2l2(l2/mr2 + 1mr˙2 GmM/r) 2 e = 1+ − (7) s mk2 ˙2 We want e < 1 and real. If we let the angular momentum l = mrθ and k = mMG, the equation for e is r6θ˙4 +r˙2r4θ˙2 2GMr3θ˙2 e = 1+ − (8) s M2G2 ˙ To simplify this equation, we can use θ = r˙/r. The equation for e becomes 2r2r˙4 2rr˙2 e = 1+ (9) s M2G2 − MG 2 From rotational Newtonian physics GM = r˙ r, then then the galactic well 2 will deepen as M r˙ or M r. The last term in equation 9 becomes 8 2 2 ∝ ∝ r˙ /M G . When this term is dominant, it will allow capturing matter with 4 r˙ to increase as the fourth power when the galactic black hole M increases. Theblack holecapturing cross sectional areaM M since bothscale csa gravity 2 ∝ as r . To explain why the Tully-Fisher and Ferrarese-Merritt equations do not exactly relate the galactic luminosity or nuclear black hole mass to the circular velocity to the fourth power, we note the following. During galaxy formation matter will be accreted onto the galactic nucleus depending on collisional losses, ionized plasma repulsion and magnetic interference. Any of these factors along with a trajectory directed within ten schwarzschild radii of the nucleus (as described below), will lead to accretion with resultant quasar or active galactic nuclear manifestations. Some decrease in the fourth power of circular velocity will result in Tully-Fisher equations as well as an increase in Ferrarese-Merritt as matter is transferred to the black hole. Elliptical galaxies, probably formed by galactic mergers, still can exhibit similar properties. 4 Trajectories Within Ten Schwarzschild Radii Effective potential for motion in Schwarzschild geometry[4] with a mass M, energy inunits of rest mass µ ofthe particle isE˜ = E/µandangular momentum is L˜ = L/µ. The quantity r in the next equations is the Schwarzschild coordinate. dr ( )2+V˜2(r) = E˜2 (10) dτ and therefore V˜2 = (1 2M/R)(1+L˜2/r2) (11) − Stable orbits are possible for L˜ > 2√3M. It should be remembered that the above equations are for nonrotating or slowly rotating black holes. For an unbound orbit, the impact parameter b is b = L˜/ (E˜2 1) (12) − q The capturing cross section for a nonrelativistic particle 2 2 σ = 16πM /β (13) capt where β is the velocity relative to light. For relativistic particles 2 2 σ = 27πM (1+ ) (14) capt 3E˜2 5 5 Discussion Could cold matter similar to baryons be the proverbial dark matter? There is much evidence that this is indeed the case. With entirely hot models of the big bang such as inflation, no such possibility could be considered. Yet a cold shell along with hot core matter can explain galaxy formation. The following galaxy formation problems[7] are solved by the capture of core and shell matter by primordial supermassive black holes originating in the shell. This model explains why the circular orbital speed from luminous matter, which dominates the inner regions, is so similar to dark matter at larger radii. With manystarsinthecenterareas,initialconditionsfordarkandluminousmatter no longer have to be closely adjusted to produce a flat rotation curve. A core based blast wave captured by the same size black holes explains why there are similiar circular speeds in all galaxies of a given luminosity no matter how the luminous matter is spaced. The overall mass to light ratio rises with decreasing surface brightness so as to preserve the Tully-Fisher relation between total luminosity and circular speed. The depth of the gravitational well determines the circular speed and luminosity as noted above. The hot and cold matter discrepancies are detectable only at accelerations below 10−8cm/secsincetheyareallbaryons. Thehaloparametersarerelatedtoth∼e luminous mass distribution since all were captured by a given size black hole. The angular momentum of collapse models are an order of magnitude less than that observed since collapse dynamics were never involved. The peak phase space density of the halo varies so markedly. This is the case since dark matter is not collisionless and not homogeneously distributed. Both shell and core matter are included. The predicted circular speed at a given luminosity is high. This is caused by the capture with the slower velocity matter gaining kinetic energy during a fall into the gravitational well. It is not directly related to mass to light ratio or halo density. The number of predicted subclumps in the halos is so much greater than observed as well as predicted clumps compared to satellite galaxies because of capturing rather than collapse dyamics. The luminosity is related to circular velocity to the fourth power. The galaxy formation process is so efficient because the blackholesactedlikevacuumcleaners removing intergalacticandintercluster matter as the universe expanded. Supermassive black holes can be formed from shell fragments. It takes a different model of the big bang to solve seemingly insurmountable problems of galaxy formation. Evidence for early galaxy formation at 6 z > 6 in Hubble and deep Herschel fields has been published[8]. Only a model whose galaxies are built upward from the massive central black holes could explain all the interelated parameters. This paper is an update from astro-ph/0012023. References [1] Bahcall, N., et al. Science, 284, 1491 (1999) [2] Goldstein, H., Classical Mechanics, Addison-Wesley Publishing Co., Reading Mass., 1980 [3] Merritt, D. and Ferrarese, L. 2000, astro-ph/0008310 [4] Misner, C., Thorne, K.S., and Wheeler, J.A. Gravitation W.H. Freeman and Co. New York 1973 [5] Peebles, P.J.E. 2000, astro-ph/9910234 [6] Disney, M.J., et al. Nature, 455, 1082 (2008) [7] Sellwood, J.A. and Kosowsky A. in Gas and Galaxy Evolution, ASP Conference Series 2000. [8] Shanks, T. et al, 2000 astro-ph/0011400 [9] Spergel, D.N. and Steinhardt, P.J. 1999, astro-ph/9909386 7